SCIENCE ABSOLUTE OF SPACE. 



11 



ily that the hemi-planes MAP and NBD inter 

 sect if the vsum of the interior angles which 

 they make with MABN is &amp;lt;st.Z. 



10. If both BN and CPU ^AM; also is 



BNII =^CP. 



For either MAB 

 and MAC make an 

 angle, or they are in 

 a plane. 



&quot;c If the first; let the 

 hemi-plane QDF bi 

 sect J_ sect AB; then 

 DQj_AB, and so DQ 

 II AM ( 8) ; likewise if hemi-plane ERS bisects 

 1 sect AC, is ER II AM; whence ( 7) DQ II ER. 

 Hence follows easily (by 9), the hemi- 

 planes ODF and ERS intersect, and have ( 7) 

 their intersection FS II DQ, and (on account of 

 BNIIDQ) also FS II BN.~ Moreover (for any 

 point of FS) FB-FA=FC, and the straight 

 FS falls in the plane TGF, bisecting 1 sect BC. 

 But (by 7) (since FS II BN) also GT II BN. 

 In the same way is proved GT II CP. Mean 

 while GT bisects J_ sect BC; and so TGBN^ 

 TGCP (1), andBNll^CP. 



If BN, AM and CP are in a plane, let (fall 

 ing without this pUine) FS II =^AM; then (from 



